Question

Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 141 minutes with a standard deviation of 12 minutes. Consider 49 of the races. Let X = the average of the 49 races. Part (a) Give the distribution of X. (Round your standard deviation to two decimal places.) X ~ , Part (b) Find the probability that the runner will average between 138 and 142 minutes in these 49 marathons. (Round your answer to four decimal places.) Part (c) Find the 80th percentile for the average of these 49 marathons. (Round your answer to two decimal places.) min Part (d) Find the median of the average running times. min

Answer 1

µ = 141

sd = 12

n = 49

a) X will be a normal distribution.

Mean of X = µ = 141

Standard deviation of X = sd / sqrt(n) = 12 / sqrt(49) = 1.714

X ~ N (141, 1.714²)

b)

                                             

                                              = P(-1.75 < Z < 0.58)

                                              = P(Z < 0.58) - P(Z < -1.75)

                                              = 0.7190 - 0.0401

                                              = 0.6789

c)

or, x = 141 + 0.84 * 12/7

or, x = 142.44

d) median = mean = 141